At slow heart rates in healthy hearts, the cardiac action potential (AP) in any given cell has a relatively constant duration on a beat-to-beat basis. Degeneration of this normal period-1 AP rhythm into higher-period or aperiodic rhythms may be closely linked to the initiation of spatiotemporal cardiac arrhythmias such as fibrillation.
Many of these cardiac arrhythmias can be characterized on the basis of the physical principles of nonlinear dynamics. Model-independent nonlinear dynamical control techniques therefore have been applied to periodic and aperiodic cardiac rhythms in an attempt to control these rhythm disturbances to restore the normal period-1 behavior.
Many of the model-independent control techniques that have previously been used to control cardiac dynamics stem from the Ott-Grebogi-Yorke (OGY) technique for controlling chaotic systems. OGY chaos control, however, requires sufficient observation of the chaotic system trajectory prior to the initiation of control so that the dynamics of the system can be learned. This allows the control algorithm to estimate the location and stability characteristics of the period-1 fixed point of the system. Control is then initiated by applying small perturbations to an accessible system parameter in an attempt to force the state of the system towards the period-1 fixed point. Applied to the heart, the most accessible system parameter available for perturbation is the timing of the next excitation, which can be advanced or (in some situations) delayed through low-magnitude current stimulation. The period between successive excitations is commonly referred to as the basic cycle length (BCL).
OGY-type control algorithms have been applied to rabbit ventricle preparations exhibiting pharmacologically induced, aperiodic (possibly chaotic) interbeat intervals. The aperiodic nature of the rhythm allowed the electrophysiological dynamics to be learned, because the system repeatedly visited the neighborhood of the target period-1 fixed point. The inter-beat intervals were successfully controlled to a period-3 rhythm, but the desired period-1 rhythm was not obtained. In another study of aperiodic dynamics, a cardiac-specific control algorithm applied to a simulated chaotic action potential duration (APD) time series was successful in controlling to the unstable period-1 rhythm at certain excitation rates.
The control algorithms used in both of the aforementioned studies require pre-control learning stages. Such learning stages may be clinically unacceptable because they could result in a dangerous delay in the termination of an arrhythmia. An additional problem with algorithms requiring a learning stage is that they are not generally applicable to stable periodic rhythms; For example, period-2 or higher-period rhythms typically do not visit the neighborhood of the unstable period-1 fixed point, and thus do not provide sufficient information for learning the stability characteristics of the period-1 fixed point. This problem is critical given that controlling periodic cardiac rhythms such as alternans (a period-2 alternation in the duration of a particular cardiac measurement) may be important, as experiments and computational models have demonstrated such rhythms to be causally linked to conduction block and the initiation of reentry.
Chaos control techniques that do not require a learning stage have thus been developed to control periodic systems. Delayed feedback control (DFC) algorithms have been used in a variety of modeling and experimental studies. These methods typically require (i) knowledge of the state of the system for a short time history, and (ii) a basic understanding of the system dynamics to ensure that the control perturbations are of the correct magnitude and polarity. These two elements allow the periodic rhythm to be stabilized by continuous adjustment of the accessible system parameter.
Both unrestricted DFC (which allow both lengthening and shortening of the BCL during control) and restricted DFC algorithms (which allow only shortening of the BCL) have been applied to cardiac rhythm disturbances. Unrestricted DFC has been used experimentally to control APD alternans in bullfrog heart preparations. Provided that the feedback proportionality constant in the algorithm was within an appropriate range of values, the period-2 alternans rhythm was successfully controlled to the underlying unstable period-1 rhythm. Unrestricted DFC has also been applied to control spatiotemporal APD alternans in simulated 1-dimensional Purkinj e fibers.
Restricted DFC algorithms have been used to control atrio-ventricular (AV) node conduction alternans, a beat-to-beat alternation in the conduction time through the AV node, in rabbit heart preparations in vitro and human subjects in vivo. In both cases, AV node conduction alternans was successfully controlled to the underlying unstable period-1 fixed point. Restricting the control scheme to apply only unidirectional (shortening) perturbations to the excitation rate was found to increase the range of values of the feedback proportionality constant over which the period-1 fixed point could be stabilized.
When DFC algorithms are used to control periodic rhythms, rapid convergence to the period-1 rhythm is achievable only if the feedback proportionality constant is at or near an optimal value that is not known a priori. The optimal value of the feedback constant is a function of the degree of instability of the fixed point, making determination of the optimal value during periodic rhythms difficult. Algorithms containing a learning stage, during which external perturbations are applied to the system in order to explore the neighborhood of the period-1 fixed point, can be used to estimate this optimal value. Another limitation of existing DFC algorithms is that they fail if the proportionality constant lies outside an acceptable range of values that is not known a priori. While algorithms that iteratively adapt the feedback constant to achieve control do exist, such algorithms are sensitive to the noise and nonstationarities that are typically present in experiments.
Existing model-independent algorithms for the control of cardiac electrophysiological dynamics all share the OGY requirement of estimating some characteristics of the fixed-point dynamics. Although such algorithms have proved effective for controlling APD alternans, an alternative approach that requires no assumptions or estimations of the fixed-point dynamics is desirable.
The invention provides such an approach. These and other advantages of the invention, as well as additional inventive features, will be apparent from the description of the invention provided herein.